English

On the fifth Whitney cone of a complex analytic curve

Algebraic Geometry 2021-08-20 v2 Complex Variables

Abstract

From a procedure to calculate the C5C_5-cone of a reduced complex analytic curve XCnX \subset \mathbb{C}^n at a singular point 0X0 \in X, we extract a collection of integers that we call {\it auxiliary multiplicities} and we prove they characterize the Lipschitz type of complex curve singularities. We then use them to improve the known bounds for the number of irreducible components of the C5C_5-cone. We finish by giving an example showing that in a Lipschitz equisingular family of curves the number of planes in the C5C_5-cone may not be constant.

Keywords

Cite

@article{arxiv.2106.14106,
  title  = {On the fifth Whitney cone of a complex analytic curve},
  author = {Arturo Giles Flores and Otoniel Nogueira da Silva and Jawad Snoussi},
  journal= {arXiv preprint arXiv:2106.14106},
  year   = {2021}
}